Comments:

So *technically* incorporeal (subtype) makes you immune to precision based damage, only overcome by ghost touch weapons. I'm not sure why they didn't say ghost touch weapon instead of force, except I must assume they weren't super familiar with the expected lingo.
To be clear, I'd count that as what was intended though.

The method with which you deal sneak attack damage modifies the way that damage is dealt. By dealing sneak attack damage with a weapon that is dealing only force damage (and not simply additional force damage) or by dealing attacking with a spell that has an attack roll against a flat footed opponent, your sneak attack becomes that sort of damage.

More over incorporeal creatures are not immune to sneak attack in pathfinder. Very, very few things are. So in fact the ninja can deal sneak attack damage to a ghost, though suffering the normal limitations any damage is dealt to a spirit. That latter part is overcome by force damage though meaning she'll do an extra 2d6 damage against it per hit.

Check the incorporeal subtype. (http://www.d20pfsrd.com/bestiary/rules-for-monsters/creature-types#subtype-incorporeal)
It specifically makes things immune to precision damage. It wouldn't matter if it was precision force damage (only by strict rules of course, it's perfectly reasonable for it to apply)
The subtype is different from just being incorporeal, though in many cases it will overlap.

Strangely enough the other section describing Incorporeal says nothing of the sort. I imagine either a discrepancy based on errata or the fact that it is a specific edition to creatures with an incorporeal subtype that is not applied to everything incorporeal.

I think it is possible to be incorporeal without having the subtype, like if it happens through a spell... but maybe you can only go ethereal through a spell. Which is a whole other can of worms. Anyway, the information should probably be in one place instead of in monster rules + subtype, unless they actually intend for the case where you can get one and not the other.

kind of curious how "Force: Spells with the force descriptor create or manipulate magical force. Force spells affect incorporeal creatures normally (as if they were corporeal creatures)." under www.d20pfsrd.com/magic#TOC-Magic-Descriptor-Force is interpreted as it refers to the incorporeal subtype being treated as corporeal. would that mean it would negate all aspects of the subtype in respect to the damage source, as its not referencing the trait.

It is the failing of the 3rd party to state what sort of action activates the Ghostslayer ability. More typically activating a ninja trick is a swift action, with rare exceptions.

Personally I can see the appeal of having the Forgotten Trick, but having to spend 2 additional ki on top of the regular cost for a ninja trick is harsh. That said, the versatility, particularly if you get the extra ki feature, makes it astoundingly useful.